Solid waste management has always been a serious problem for cities throughout the world. Municipal solid waste management is one among the fundamental and essential services provided by municipal authorities in the country to keep urban centres clean. For better urban solid waste management, efficient waste collection and dumping system are required. Graph theory plays an important role in solving different problems where classical mathematics has some limitations. It has many applications and has proven to be an extremely useful tool in analysing various practical problems. In this paper, application of graph theory in municipal solid waste management is depicted. Solid waste management of three municipal areas of West Bengal is considered as test bed cases. The proposed method in this paper have the prospective to find the feasible solution not only in these three municipal areas but also in other transient economies where sustainable waste management practices are yet to meet a critical mass of success and it should be supported at all levels for waste minimisation and its proper utilisation.